Question

the pre-image, δstu, has undergone a type of transformation called a rigid transformation to produce the image, δvwx. compare the measures of the triangles by dragging the image to the pre-image. which measures are equal? check all that apply. st = vw su = vx tu = wx m∠sut = m∠vxw m∠tsu = m∠wvx m∠uts = m∠xwv

Explanation:

Step1: Recall Rigid Transformation Properties

A rigid transformation (translation, rotation, reflection) preserves side lengths and angle measures of a figure. So corresponding sides and corresponding angles of the pre - image ($\triangle STU$) and image ($\triangle VWX$) are equal.

Step2: Identify Corresponding Parts

• For sides:
• Side $ST$ in $\triangle STU$ should correspond to side $VW$ in $\triangle VWX$, so $ST = VW$.
• Side $SU$ in $\triangle STU$ should correspond to side $VX$ in $\triangle VWX$, so $SU=VX$.
• Side $TU$ in $\triangle STU$ should correspond to side $WX$ in $\triangle VWX$, so $TU = WX$.
• For angles:
• $\angle SUT$ in $\triangle STU$ corresponds to $\angle VXW$ in $\triangle VWX$, so $m\angle SUT=m\angle VXW$.
• $\angle TSU$ in $\triangle STU$ corresponds to $\angle WVX$ in $\triangle VWX$, so $m\angle TSU = m\angle WVX$.
• $\angle UTS$ in $\triangle STU$ corresponds to $\angle XWV$ in $\triangle VWX$, so $m\angle UTS=m\angle XWV$.

Answer:

• $ST = VW$
• $SU = VX$
• $TU = WX$
• $m\angle SUT=m\angle VXW$
• $m\angle TSU = m\angle WVX$
• $m\angle UTS=m\angle XWV$